Exam 84

Exam questions and solutions in LaTex

¿Pueden pensar las máquinas? Una evaluación del problema de la inteligencia artificial mediante el equilibrio refractivo

Revisión del problema de la filosofía de la Inteligencia Artificial a la vista del Equilibrio refractivo. La revisión del problema se lleva a cabo para mostrar como "¿pueden pensar las máquinas?" sólo se ha evaluado en los terminos humanos. El equilibrio refractivo se plantea como una herramienta para definir conceptos de tal modo que la experiencia y los preceptos se encuentren en equilibrio, para con él construir una definición de pensar que no esté limitada exclusivamente a "pensar tal y como lo hacen los humanos".

Iteración de funciones e introducción al caos con Mathematica.

Estudio de la iteración de punto fijo muy habitual en todos los programas de cálculo numérico y su aplicación en el caso de la función logística. Se introducen así elementos característicos de la teoría del caos, como son el efecto mariposa o el exponente de Lyapunov. La experiencia se llevó a cabo en la Escuela de Ingeniería Técnica Industrial de Córdoba. El software utilizado fue Mathematica debido a su gran versatilidad. El iterador de punto fijo se utiliza en biología para modelar el crecimiento en determinadas poblaciones.

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two–sided many–to–many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 – Example 1), nor to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1 – Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Does Opaqueness Make Equity Capital Expensive for Banks?

Bank managers often claim that equity is expensive, which contradicts the Modigliani-Miller irrelevance theorem. An opaque bank must signal its solvency by paying high and stable dividends in order to keep depositors tranquil. This signalling may require costly liquidations if the return on assets has been poor, but not paying the dividend might trigger a run. A strongly capitalized bank should keep substantial amounts of risk-free yet non-productive currency because the number of shares is high, which is costly. The dividend is informative of the state of the bank; rational depositors react to it.

Does uncertainty cause inertia in decision making? An experimental study of the role of regret aversion and indecisiveness

Previous research has shown that often there is clear inertia in individual decision making---that is, a tendency for decision makers to choose a status quo option. I conduct a laboratory experiment to investigate two potential determinants of inertia in uncertain environments: (i) regret aversion and (ii) ambiguity-driven indecisiveness. I use a between-subjects design with varying conditions to identify the effects of these two mechanisms on choice behavior. In each condition, participants choose between two simple real gambles, one of which is the status quo option. I find that inertia is quite large and that both mechanisms are equally important.

Risk, ambiguity, and diversification

Attitudes toward risk influence the decision to diversify among uncertain options. Yet, because in most situations the options are ambiguous, attitudes toward ambiguity may also play an important role. I conduct a laboratory experiment to investigate the effect of ambiguity on the decision to diversify. I find that diversification is more prevalent and more persistent under ambiguity than under risk. Moreover, excess diversification under ambiguity is driven by participants who stick with a status quo gamble when diversification among gambles is not feasible. This behavioral pattern cannot be accommodated by major theories of choice under ambiguity.

New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

Robust Control of Systems Subjected to Uncertain Disturbances and Actuator Dynamics

Esta tesis está enfocada al diseño y validación de controladores robustos que pueden reducir de una manera efectiva las vibraciones structurales producidas por perturbaciones externas tales como terremotos, fuertes vientos o cargas pesadas. Los controladores están diseñados basados en teorías de control tradicionalamente usadas en esta area: Teoría de estabilidad de Lyapunov, control en modo deslizante y control clipped-optimal, una técnica reciente mente introducida : Control Backstepping y una que no había sido usada antes: Quantitative Feedback Theory. La principal contribución al usar las anteriores técnicas, es la solución de problemas de control estructural abiertos tales como dinámicas de actuador, perturbaciones desconocidas, parametros inciertos y acoplamientos dinámicos. Se utilizan estructuras típicas para validar numéricamente los controladores propuestos. Especificamente las estructuras son un edificio de base aislada, una plataforma estructural puente-camión y un puente de 2 tramos, cuya configuración de control es tal que uno o mas problemas abiertos están presentes. Se utilizan tres prototipos experimentales para implementar los controladores robustos propuestos, con el fin de validar experimentalmente su efectividad y viabilidad. El principal resultado obtenido con la presente tesis es el diseño e implementación de controladores estructurales robustos que resultan efectivos para resolver problemas abiertos en control estructural tales como dinámicas de actuador, parámetros inciertos, acoplamientos dinámicos, limitación de medidas y perturbaciones desconocidas.

Unimodality of wave amplitude in the northern Hemisphere

A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960-2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality. The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960-70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude. As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.

Acoustic scattering by mildly rough unbounded surfaces in three dimensions

For a nonlocally perturbed half- space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard ansatz as a combined single-and double-layer potential but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half- space Green's function. Due to the unboundedness of the surface, the integral operators are noncompact. In contrast to the two-dimensional case, the integral operators are also strongly singular, due to the slow decay at infinity of the fundamental solution of the three-dimensional Helmholtz equation. In the case when the surface is sufficiently smooth ( Lyapunov) we show that the integral operators are nevertheless bounded as operators on L-2(Gamma) and on L-2(Gamma G) boolean AND BC(Gamma) and that the operators depend continuously in norm on the wave number and on G. We further show that for mild roughness, i.e., a surface G which does not differ too much from a plane, the boundary integral equation is uniquely solvable in the space L-2(Gamma) boolean AND BC(Gamma) and the scattering problem has a unique solution which satisfies a limiting absorption principle in the case of real wave number.

Beurling zeta functions, generalised primes, and fractal membranes

We study generalised prime systems P (1 < p(1) <= p(2) <= ..., with p(j) is an element of R tending to infinity) and the associated Beurling zeta function zeta p(s) = Pi(infinity)(j=1)(1 - p(j)(-s))(-1). Under appropriate assumptions, we establish various analytic properties of zeta p(s), including its analytic continuation, and we characterise the existence of a suitable generalised functional equation. In particular, we examine the relationship between a counterpart of the Prime Number Theorem (with error term) and the properties of the analytic continuation of zeta p(s). Further we study 'well-behaved' g-prime systems, namely, systems for which both the prime and integer counting function are asymptotically well-behaved. Finally, we show that there exists a natural correspondence between generalised prime systems and suitable orders on N-2. Some of the above results are relevant to the second author's theory of 'fractal membranes', whose spectral partition functions are given by Beurling-type zeta functions, as well as to joint work of that author and R. Nest on zeta functions attached to quasicrystals.

Force constants and dipole moment derivatives of molecules from perturbed Hartree-Fock calculations II. Applications to limited basis set SCF-MO wavefunctions

The perturbed Hartree–Fock theory developed in the preceding paper is applied to LiH, BH, and HF, using limited basis‐set SCF–MO wavefunctions derived by previous workers. The calculated values for the force constant ke and the dipole‐moment derivative μ(1) are (experimental values in parentheses): LiH, ke  =  1.618(1.026)mdyn/Å,μ(1)  =  −18.77(−2.0±0.3)D/ÅBH,ke  =  5.199(3.032)mdyn/Å,μ(1)  =  −1.03(−)D/Å;HF,ke  =  12.90(9.651)mdyn/Å,μ(1)  =  −2.15(+1.50)D/Å. The values of the force on the proton were calculated exactly and according to the Hellmann–Feynman theorem in each case, and the discrepancies show that none of the wavefunctions used are close to the Hartree–Fock limit, so that the large errors in ke and μ(1) are not surprising. However no difficulties arose in the perturbed Hartree–Fock calculation, so that the application of the theory to more accurate wavefunctions appears quite feasible.